Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-2y &= 5 \\ x+2y &= 6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = -x+6$ Divide both sides by $2$ to isolate $y$ $y = {-\dfrac{1}{2}x + 3}$ Substitute this expression for $y$ in the first equation. $2x-2({-\dfrac{1}{2}x + 3}) = 5$ $2x + x - 6 = 5$ Simplify by combining terms, then solve for $x$ $3x - 6 = 5$ $3x = 11$ $x = \dfrac{11}{3}$ Substitute $\dfrac{11}{3}$ for $x$ back into the top equation. $2( \dfrac{11}{3})-2y = 5$ $\dfrac{22}{3}-2y = 5$ $-2y = -\dfrac{7}{3}$ $y = \dfrac{7}{6}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = \dfrac{7}{6}$.